LEDs are bad for battery. I'm not sure how much a modern, small LED uses, but the old style 'big' LEDs would use some 20mA. If you run that LED for 30 days it would have used 14.4 ampere hours, which is enough to make a bad dent even in a car battery. I know someone with a solar-powered cottage who came to the cottage and found a flat battery, not because of the fact that there hadn't been any sun, but because the charger circuit had a nice big LED.

I once made the mistake of installing an application on my Palm T3 which would turn on its tiny LED if the battery level got too low, as a warning. Talk about stupid.. I had left the T3 at home over the weekend and on Monday it was flat and all my data and applications were wiped out (normally it would have lasted probably a week, at least, in that condition).